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The information-based complexity of approximation problem by adaptive Monte Carlo methods 被引量:2
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作者 FANG GenSun DUAN LiQin 《Science China Mathematics》 SCIE 2008年第9期1679-1689,共11页
In this paper, we study the complexity of information of approximation problem on the multivariate Sobolev space with bounded mixed derivative MW p,α r ( $ \mathbb{T}^d $ ), 1 < p < ∞, in the norm of L q ( $ \... In this paper, we study the complexity of information of approximation problem on the multivariate Sobolev space with bounded mixed derivative MW p,α r ( $ \mathbb{T}^d $ ), 1 < p < ∞, in the norm of L q ( $ \mathbb{T}^d $ ), 1 < q < ∞, by adaptive Monte Carlo methods. Applying the discretization technique and some properties of pseudo-s-scale, we determine the exact asymptotic orders of this problem. 展开更多
关键词 adaptive Monte Carlo method Sobolev space with bounded mixed derivative asymptotic order 41A46 41A63 65c05 65D99
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Bounds on the clique-transversal number of regular graphs 被引量:5
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作者 CHENG T.C.E 《Science China Mathematics》 SCIE 2008年第5期851-863,共13页
A clique-transversal set D of a graph G is a set of vertices of G such that D meets all cliques of G. The clique-transversal number, denoted τ c (G), is the minimum cardinality of a clique-transversal set in G. In th... A clique-transversal set D of a graph G is a set of vertices of G such that D meets all cliques of G. The clique-transversal number, denoted τ c (G), is the minimum cardinality of a clique-transversal set in G. In this paper we present the bounds on the clique-transversal number for regular graphs and characterize the extremal graphs achieving the lower bound. Also, we give the sharp bounds on the clique-transversal number for claw-free cubic graphs and we characterize the extremal graphs achieving the lower bound. 展开更多
关键词 graph regular graph claw-free cubic graph clique-transversal set clique-transversal number 05C65 05C69 05C75
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